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Properties

Label 126.9.i
Level $126$
Weight $9$
Character orbit 126.i
Rep. character $\chi_{126}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Sturm bound $216$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 126.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(216\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(126, [\chi])\).

Total New Old
Modular forms 392 128 264
Cusp forms 376 128 248
Eisenstein series 16 0 16

Trace form

\( 128 q + 8192 q^{4} + 512 q^{6} - 1846 q^{7} + 11164 q^{9} + O(q^{10}) \) \( 128 q + 8192 q^{4} + 512 q^{6} - 1846 q^{7} + 11164 q^{9} + 3370 q^{13} - 94464 q^{14} + 68482 q^{15} - 1048576 q^{16} - 63450 q^{17} + 254976 q^{18} - 185108 q^{19} + 444040 q^{21} + 32768 q^{24} - 10000000 q^{25} + 1262592 q^{26} - 513450 q^{27} + 236288 q^{28} + 948816 q^{29} + 633088 q^{30} + 71392 q^{31} - 4167178 q^{33} - 6977790 q^{35} - 458240 q^{36} - 546986 q^{37} + 2620702 q^{39} + 2151648 q^{41} - 2156544 q^{42} + 1131328 q^{43} - 4372992 q^{44} - 1314430 q^{45} + 3708672 q^{46} - 6602256 q^{47} - 7123798 q^{49} + 11082240 q^{50} + 10335110 q^{51} + 862720 q^{52} + 3636216 q^{53} + 1193984 q^{54} + 13193184 q^{55} + 15120510 q^{57} - 15705600 q^{58} + 48255390 q^{59} + 25605376 q^{60} + 841954 q^{61} - 6229626 q^{63} - 268435456 q^{64} - 87167934 q^{65} - 31015936 q^{66} - 22149890 q^{67} - 5746894 q^{69} - 34359552 q^{70} - 2162688 q^{72} + 23745988 q^{73} - 34216394 q^{75} + 23693824 q^{76} - 114371586 q^{77} + 3633152 q^{78} + 12032254 q^{79} - 174409268 q^{81} + 113778688 q^{84} - 57202500 q^{85} - 308940506 q^{87} - 310432014 q^{89} - 70782976 q^{90} - 146880002 q^{91} + 8752896 q^{92} - 602184854 q^{93} - 23665152 q^{94} - 541747728 q^{95} - 4194304 q^{96} - 57564566 q^{97} - 247163904 q^{98} + 190993138 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{9}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)